Question

Maeva is standing 40 meters from the foot of a tree. Her line of sight to the top of the tree forms an angle of elevation of 55°. Find the approximate height of the tree above Maeva’s line of sight.(1 point) Responses 46.15 m 46.15 m 28.01 m 28.01 m 65.55 m 65.55 m 57.13 m

Answer 1

To find the height of the tree above Maeva's line of sight, we can use trigonometric functions. Specifically, we can use the tangent function, which relates the height of the tree to the distance Maeva is standing from the base of the tree and the angle of elevation.

Let:
- \( h \) = height of the tree above Maeva's line of sight,
- \( d \) = distance from Maeva to the tree (40 meters),
- \( \theta \) = angle of elevation (55°).

The tangent of the angle theta is defined as:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d}
\]

Plugging in the values:

\[
\tan(55°) = \frac{h}{40}
\]

To find \( h \):

\[
h = 40 \cdot \tan(55°)
\]

Now calculating this:

1. Calculate \( \tan(55°) \):
\[
\tan(55°) \approx 1.4281
\]

2. Now plug this value into the equation for \( h \):
\[
h \approx 40 \cdot 1.4281 \approx 57.13 \text{ m}
\]

Thus, the approximate height of the tree above Maeva’s line of sight is **57.13 m**.